There is... something though that separates man from animal. Something about our method of cognition. That’s what my personal intuition tells me, surely influenced by my religious beliefs.
Scientific thinking says that man is just a smart ape, it very well may be.
Humans have two centers of consciousness; inner self and the ego. Animals have one center of consciousness; inner self. The inner self is much older than the ego and is connected to our DNA. It is the center of consciousness for instinct and collective species behavior; human nature or lion nature. The inner self has a very 3-D view of reality; integrated with nature.
The ego is much newer and may have appeared only about 6-10k years ago. It offers a secondary POV, that can either reinforce or depart from the inner self. Humans have lost much of their natural instinct in favor of culture and artificial instincts, via the ego. Since the inner self is connected to our DNA, it remains even with the ego, but tends to get more unconscious to the ego. Transgender is from the ego, since the inner self is a product of our DNA. The ego can oppose the inner self.
The possible exception to the two or one center of consciousness dividing line, between humans and animals, are domesticated animals, like dogs. These highly species appear to have the potential for a virtual secondary, that can be induced with the outside via human help. The dog owner who treats their dog like a spoiled baby, can induce this type of semi-human behavior, via s a virtual secondary, in spite of the dog still having natural instincts from its primary; inner self. They will play the role and even initiate the assumed spoiled needs for their owner. Ferrel dogs tend to revert back to the DNA based primary.
The term self aware is implicit of being aware of the inner self or another center of consciousness that is connected to our DNA. It often makes decisions for us that we may call, innate.
As an home experiment to witness the inner self in action, agree to have someone scare you when you are not prepared. They can take their time to catch you off guard and jump at you from behind a door. What often happens the ego is caught off guard and the inner self will react first, with instinct. Often the ego is embarrassed that it; inner self let out a squeal. It may get mad as a defense mechanism as the ego tries to save face. Outer social reality is more important to the ego than to the inner self.
The human ego has will power and choice in the sense it can choose things that would not be chosen by the DNA based inner self; natural instinct. This can be good and bad, like the tree of knowledge of good and evil. Often social definitions of good and evil are there for the ego and often these can harm or help the inner self. If they harm the inner self, this brings suffering into the world, since one is not being true to their innate nature.
In terms of evolution, the ego may not have formed by the standard mutation method, since a center of consciousness is far more complicated; firmware, than a few genes. It is an integrated phenomena that regulates the sum total of the DNA since all is connected for this pinnacle consciousness affect. This is why Genesis has Adam created in a way that was not biological. He was the first human ego.
My guess is the ego formed with the help of domesticated animals, but before they were domesticated. The pre-humans had evolved from the apes and had human DNA and human inner self; natural human. A virtual ego appeared as a result of humans learning from other animals like dogs.
In the case of dogs, both the pre-humans and dogs; wolves, were apex animals, with the dogs having unique skills that apes did not have, such as hunting in packs and a high protein diet. These new ape-man skills were not part of the original prehuman DNA. They were learned and would form a virtual secondary; monkey see monkey do. The ego would eventually consolidate. This was not an original feature of the inner self, but it allowed new selective advantages than benefited the survival of both. The ego defined modern humans as separate from the prehumans. Both has human DNA but the ego made man different.
The two trees in the Garden of Eden; Tree of Life and Tree of Knowledge of Good and Evil, where connected to the inner self and ego, respectively; neurons branchings. The tree of life is how the inner self was a product of natural selection and DNA. The tree of knowledge was connected to the external learning nature of the ego, as it tries to substitutive learned knowledge for the objective nature of the inner self. Inventions like spoken and written language would go a long way to consolidate the ego; external learning.